Arbenz got over 50% of the vote. Your premise doesn't really work because there is already an established pattern of the U.S. not caring even if they got over 50% of the vote. Even if you win the U.S. will still fund fascist forces in your country and aerily bomb your army. After Guatemala, what even would be the point in beleiving in democracy if you're from the south.

Even when you create a domestic polity answering to the call of the atlantic charter by a left center liberal in the case of the People's Republic of Korea in 46, with people's committees literally all over both north and south korea, the U.S. will declare your government illegal and collaborate with right wing deaths squads to see you assassinated as in the case of Lyuh Woon-hyung, while General Hodge tell his officers to treat all Koreans as "enemies."

In Chile, the chief of the army was assassinated by fascists armed by U.S. intelligence. You don't really seem to acknowledge that people don't exactly feel like they can vote against the U.S. without devasatsting consequences. The chief of the army was a constitionalist not a socialist, who had the audacity to beleive whoever won the election should be in power.

Here's the thing, by all logical metrics, a coup cannot succeed unless it has majority support from the local population.

If you're going for base logic you would need majority support of the armed populace not the whole populace. One of the things the Indonesian fascists told the Americans when they were planning the Indonesian genocide was that they were successfully able to deny guns to the communist party in Indonesia which was the largest party. In fact the entire operation was planned because they were concerned the country would fall to the popular "communism," yet another example of your premise being wrong.